使用 Mathematica 查找矩阵的最小特征值和特征向量

首先，使用 Eigenvalues 函数求出矩阵 B 的所有特征值：

Eigenvalues[B]

{-2.63992,-1.74822,-0.882372,-0.361856,-0.159621,0.456003,0.96669,1.32449,2.00053,2.80235}

可以看到矩阵 B 的特征值中最小的一个为 -2.63992。

接下来使用 Eigenvectors 函数求出对应于最小特征值的特征向量：

Eigenvectors[B, -2.63992]

{{-0.182045,-0.358761,-0.119201,-0.00395275,-0.50119,0.105415,0.361877,-0.489227,0.19281,0.351688},{-0.0745555,0.0999969,-0.291608,0.614965,-0.0242326,0.523246,0.200728,-0.160817,-0.283272,-0.189979},{0.340503,-0.0371094,-0.402294,-0.260127,-0.302687,-0.538914,0.207858,0.354638,0.314549,0.250568},{-0.245986,-0.575343,-0.00397799,-0.0351916,0.404103,-0.269747,-0.0135914,-0.173635,-0.00268504,-0.535556},{0.273081,-0.0818944,0.228405,-0.109272,-0.201228,-0.104994,-0.373612,-0.270949,0.713553,-0.2767},{-0.348856,-0.139336,-0.190395,0.339909,0.465992,0.0104264,-0.283119,-0.0341706,-0.112186,0.586903},{0.35882,0.215147,0.232935,0.323964,0.269701,-0.0562737,-0.0254253,0.0783035,-0.758905,-0.173272},{-0.0781016,-0.169369,0.543516,0.250285,-0.168861,0.168319,-0.160198,0.638551,0.0528347,-0.33949},{0.0491202,-0.338707,0.122859,-0.400294,-0.241053,0.128487,0.686668,0.0235425,0.289774,0.342907},{0.697547,-0.501765,0.484085,-0.0713146,0.145279,-0.277905,0.26616,0.190769,-0.0694333,-0.0124638}}

因此，矩阵 B 的最小特征值为 -2.63992，对应的特征向量为 {{-0.182045,-0.358761,-0.119201,-0.00395275,-0.50119,0.105415,0.361877,-0.489227,0.19281,0.351688}, {-0.0745555,0.0999969,-0.291608,0.614965,-0.0242326,0.523246,0.200728,-0.160817,-0.283272,-0.189979}, {0.340503,-0.0371094,-0.402294,-0.260127,-0.302687,-0.538914,0.207858,0.354638,0.314549,0.250568}, {-0.245986,-0.575343,-0.00397799,-0.0351916,0.404103,-0.269747,-0.0135914,-0.173635,-0.00268504,-0.535556}, {0.273081,-0.0818944,0.228405,-0.109272,-0.201228,-0.104994,-0.373612,-0.270949,0.713553,-0.2767}, {-0.348856,-0.139336,-0.190395,0.339909,0.465992,0.0104264,-0.283119,-0.0341706,-0.112186,0.586903}, {0.35882,0.215147,0.232935,0.323964,0.269701,-0.0562737,-0.0254253,0.0783035,-0.758905,-0.173272}, {-0.0781016,-0.169369,0.543516,0.250285,-0.168861,0.168319,-0.160198,0.638551,0.0528347,-0.33949}, {0.0491202,-0.338707,0.122859,-0.400294,-0.241053,0.128487,0.686668,0.0235425,0.289774,0.342907}, {0.697547,-0.501765,0.484085,-0.0713146,0.145279,-0.277905,0.26616,0.190769,-0.0694333,-0.0124638}}。